The following table lists the common coordinate systems in use by the astronomical community. Thefundamental plane divides thecelestial sphere into two equalhemispheres and defines the baseline for the latitudinal coordinates, similar to theequator in thegeographic coordinate system. The poles are located at ±90° from the fundamental plane. The primary direction is the starting point of the longitudinal coordinates. The origin is the zero distance point, the "center of the celestial sphere", although the definition ofcelestial sphere is ambiguous about the definition of its center point.
Equatorial (red) and horizontal (blue) celestial coordinates
Thehorizontal, oraltitude-azimuth, system is based on the position of the observer on Earth, which revolves around its own axis once persidereal day (23 hours, 56 minutes and 4.091 seconds) in relation to the star background. The positioning of a celestial object by the horizontal system varies with time, but is a useful coordinate system for locating and tracking objects for observers on Earth. It is based on the position of stars relative to an observer's ideal horizon.
Theequatorial coordinate system is centered at Earth's center, but fixed relative to the celestial poles and theMarch equinox. The coordinates are based on the location of stars relative to Earth's equator if it were projected out to an infinite distance. The equatorial describes the sky as seen from theSolar System, and modern star maps almost exclusively use equatorial coordinates.
Theequatorial system is the normal coordinate system for most professional and many amateur astronomers having an equatorial mount that follows the movement of the sky during the night. Celestial objects are found by adjusting the telescope's or other instrument's scales so that they match the equatorial coordinates of the selected object to observe.
Popular choices of pole and equator are the olderB1950 and the modernJ2000 systems, but a pole and equator "of date" can also be used, meaning one appropriate to the date under consideration, such as when a measurement of the position of a planet or spacecraft is made. There are also subdivisions into "mean of date" coordinates, which average out or ignorenutation, and "true of date," which include nutation.
The fundamental plane is the plane of the Earth's orbit, called the ecliptic plane. There are two principal variants of the ecliptic coordinate system: geocentric ecliptic coordinates centered on the Earth and heliocentric ecliptic coordinates centered on the center of mass of the Solar System.
The geocentric ecliptic system was the principal coordinate system for ancient astronomy and is still useful for computing the apparent motions of the Sun, Moon, and planets.[3] It was used to define the twelveastrological signs of thezodiac, for instance.
The heliocentric ecliptic system describes the planets' orbital movement around the Sun, and centers on thebarycenter of the Solar System (i.e. very close to the center of the Sun). The system is primarily used for computing the positions of planets and other Solar System bodies, as well as defining theirorbital elements.
The galactic coordinate system uses the approximate plane of the Milky Way Galaxy as its fundamental plane. The Solar System is still the center of the coordinate system, and the zero point is defined as the direction towards theGalactic Center. Galactic latitude resembles the elevation above the galactic plane and galactic longitude determines direction relative to the center of the galaxy.
The supergalactic coordinate system corresponds to a fundamental plane that contains a higher than average number of local galaxies in the sky as seen from Earth.
The classical equations, derived fromspherical trigonometry, for the longitudinal coordinate are presented to the right of a bracket; dividing the first equation by the second gives the convenient tangent equation seen on the left.[5] The rotation matrix equivalent is given beneath each case.[6] This division is ambiguous because tan has a period of 180° (π) whereas cos and sin have periods of 360° (2π).
Azimuth (A) is measured from the south point, turning positive to the west.[7]Zenith distance, the angular distance along thegreat circle from thezenith to a celestial object, is simply thecomplementary angle of the altitude:90° −a.[8]
In solving thetan(A) equation forA, in order to avoid the ambiguity of thearctangent, use of thetwo-argument arctangent, denotedatan2(x,y), is recommended. The two-argument arctangent computes the arctangent ofy/x, and accounts for the quadrant in which it is being computed. Thus, consistent with the convention of azimuth being measured from the south and opening positive to the west,
,
where
.
If the above formula produces a negative value forA, it can be rendered positive by simply adding 360°.
Again, in solving thetan(h) equation forh, use of the two-argument arctangent that accounts for the quadrant is recommended. Thus, again consistent with the convention of azimuth being measured from the south and opening positive to the west,
These equations[14] are for converting equatorial coordinates to Galactic coordinates.
are the equatorial coordinates of the North Galactic Pole and is the Galactic longitude of the North Celestial Pole. Referred toJ2000.0 the values of these quantities are:
If the equatorial coordinates are referred to anotherequinox, they must beprecessed to their place at J2000.0 before applying these formulae.
These equations convert to equatorial coordinates referred toB2000.0.
Angles in the degrees ( ° ), minutes ( ′ ), and seconds ( ″ ) ofsexagesimal measure must be converted to decimal before calculations are performed. Whether they are converted to decimaldegrees orradians depends upon the particular calculating machine or program. Negative angles must be carefully handled;−10° 20′ 30″ must be converted as−10° −20′ −30″.
Angles in the hours (h ), minutes (m ), and seconds (s ) of time measure must be converted to decimaldegrees orradians before calculations are performed. 1h = 15°; 1m = 15′; 1s = 15″
Angles greater than 360° (2π) or less than 0° may need to be reduced to the range 0°–360° (0–2π) depending upon the particular calculating machine or program.
The cosine of a latitude (declination, ecliptic and Galactic latitude, and altitude) are never negative by definition, since the latitude varies between −90° and +90°.
Inverse trigonometric functions arcsine, arccosine and arctangent arequadrant-ambiguous, and results should be carefully evaluated. Use of thesecond arctangent function (denoted in computing asatn2(y,x) oratan2(y,x), which calculates the arctangent ofy/x using the sign of both arguments to determine the right quadrant) is recommended when calculating longitude/right ascension/azimuth. An equation which finds thesine, followed by thearcsin function, is recommended when calculating latitude/declination/altitude.
Azimuth (A) is referred here to the south point of thehorizon, the common astronomical reckoning. An object on themeridian to the south of the observer hasA =h = 0° with this usage. However, nAstropy's AltAz, in theLarge Binocular Telescope FITS file convention, inXEphem, in theIAU libraryStandards of Fundamental Astronomy and Section B of theAstronomical Almanac for example, the azimuth is East of North. Innavigation and some other disciplines, azimuth is figured from the north.
The equations for horizontal coordinates do not account fordiurnal parallax, that is, the small offset in the position of a celestial object caused by the position of the observer on theEarth's surface. This effect is significant for theMoon, less so for theplanets, minute forstars or more distant objects.
Observer's longitude (λo) here is measured positively eastward from theprime meridian, accordingly to currentIAU standards.
^Depending on the azimuth convention in use, the signs ofcosA andsinA appear in all four different combinations. Karttunen et al.,[9] Taff,[10] and Roth[11] defineA clockwise from the south. Lang[12] defines it north through east, Smart[13] north through west. Meeus (1991),[4] p. 89:sinδ = sinφ sina − cosφ cosa cosA;Explanatory Supplement (1961),[5] p. 26:sinδ = sina sinφ + cosa cosA cosφ.
^Majewski, Steve."Coordinate Systems". UVa Department of Astronomy. Archived fromthe original on 12 March 2016. Retrieved19 March 2011.
^Aaboe, Asger. 2001Episodes from the Early History of Astronomy. New York: Springer-Verlag., pp. 17–19.
^abMeeus, Jean (1991).Astronomical Algorithms. Willmann-Bell, Inc., Richmond, VA.ISBN0-943396-35-2., chap. 12
^abU.S. Naval Observatory, Nautical Almanac Office; H.M. Nautical Almanac Office (1961).Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac. H.M. Stationery Office, London., sec. 2A
^U.S. Naval Observatory, Nautical Almanac Office (1992). P. Kenneth Seidelmann (ed.).Explanatory Supplement to the Astronomical Almanac. University Science Books, Mill Valley, CA.ISBN0-935702-68-7., section 11.43
^Montenbruck, Oliver; Pfleger, Thomas (2000).Astronomy on the Personal Computer. Springer-Verlag Berlin Heidelberg.ISBN978-3-540-67221-0., pp 35-37
^U.S. Naval Observatory, Nautical Almanac Office; U.K. Hydrographic Office, H.M. Nautical Almanac Office (2008).The Astronomical Almanac for the Year 2010. U.S. Govt. Printing Office. p. M18.ISBN978-0160820083.
NOVAS, theUnited States Naval Observatory's Vector Astrometry Software, an integrated package of subroutines and functions for computing various commonly needed quantities in positional astronomy.
SuperNOVAS a maintained fork of NOVAS C 3.1 with bug fixes, improvements, new features, and online documentation.
SOFA, theIAU's Standards of Fundamental Astronomy, an accessible and authoritative set of algorithms and procedures that implement standard models used in fundamental astronomy.
